Practice · Distance grows in proportion to time · Sensim Math

Variant 1 easy

A car travels $12 \text{ miles } 0 \text{ yards}$ in 10 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 25 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 12 mi 0 yd in 10 minutes at a steady speed. We must find how far it goes in 25 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 25, then convert back to miles and yards.

Givens

Distance in 10 min: 12 mi 0 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 25 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 10-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 12 mi = 12 times 1760 = 21120 yd. Add the extra 0 yd to get the total in yards.

12 \times 1760 + 0 = 21120 + 0 = 21120 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 21120 yd in 10 minutes at a steady speed, so divide by 10 to get how far it goes each minute.

21120 \div 10 = 2112 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 25 minutes

#7 Identify Subproblems 4.MD.A.2

For 25 minutes, multiply the per-minute distance by 25.

2112 \times 25 = 52800 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 52800 yd by 1760 to find whole miles: 30 miles use 30 times 1760 = 52800 yd, leaving 52800 - 52800 = 0 yd. So the distance is 30 mi 0 yd.

52800 \div 1760 = 30 \text{ mi remainder } 0 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 30 mi 0 yd

4 · Reviewdoes it hold up?

25 minutes is more than 10 minutes, so the distance should be larger than 12 mi 0 yd, and 30 mi 0 yd is indeed larger. The car adds 2112 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 21120 yd covered in 10 min by $\frac{25}{10}$ to get 52800 yd = 30 mi 0 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 2 easy

A car travels $20 \text{ miles } 0 \text{ yards}$ in 20 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 30 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 20 mi 0 yd in 20 minutes at a steady speed. We must find how far it goes in 30 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 30, then convert back to miles and yards.

Givens

Distance in 20 min: 20 mi 0 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 30 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 20-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 20 mi = 20 times 1760 = 35200 yd. Add the extra 0 yd to get the total in yards.

20 \times 1760 + 0 = 35200 + 0 = 35200 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 35200 yd in 20 minutes at a steady speed, so divide by 20 to get how far it goes each minute.

35200 \div 20 = 1760 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 30 minutes

#7 Identify Subproblems 4.MD.A.2

For 30 minutes, multiply the per-minute distance by 30.

1760 \times 30 = 52800 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 52800 yd by 1760 to find whole miles: 30 miles use 30 times 1760 = 52800 yd, leaving 52800 - 52800 = 0 yd. So the distance is 30 mi 0 yd.

52800 \div 1760 = 30 \text{ mi remainder } 0 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 30 mi 0 yd

4 · Reviewdoes it hold up?

30 minutes is more than 20 minutes, so the distance should be larger than 20 mi 0 yd, and 30 mi 0 yd is indeed larger. The car adds 1760 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 35200 yd covered in 20 min by $\frac{30}{20}$ to get 52800 yd = 30 mi 0 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 3 easy

A car travels $24 \text{ miles } 0 \text{ yards}$ in 16 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 40 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 24 mi 0 yd in 16 minutes at a steady speed. We must find how far it goes in 40 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 40, then convert back to miles and yards.

Givens

Distance in 16 min: 24 mi 0 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 40 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 16-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 24 mi = 24 times 1760 = 42240 yd. Add the extra 0 yd to get the total in yards.

24 \times 1760 + 0 = 42240 + 0 = 42240 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 42240 yd in 16 minutes at a steady speed, so divide by 16 to get how far it goes each minute.

42240 \div 16 = 2640 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 40 minutes

#7 Identify Subproblems 4.MD.A.2

For 40 minutes, multiply the per-minute distance by 40.

2640 \times 40 = 105600 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 105600 yd by 1760 to find whole miles: 60 miles use 60 times 1760 = 105600 yd, leaving 105600 - 105600 = 0 yd. So the distance is 60 mi 0 yd.

105600 \div 1760 = 60 \text{ mi remainder } 0 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 60 mi 0 yd

4 · Reviewdoes it hold up?

40 minutes is more than 16 minutes, so the distance should be larger than 24 mi 0 yd, and 60 mi 0 yd is indeed larger. The car adds 2640 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 42240 yd covered in 16 min by $\frac{40}{16}$ to get 105600 yd = 60 mi 0 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 4 medium

A car travels $30 \text{ miles } 0 \text{ yards}$ in 25 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 60 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 30 mi 0 yd in 25 minutes at a steady speed. We must find how far it goes in 60 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 60, then convert back to miles and yards.

Givens

Distance in 25 min: 30 mi 0 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 60 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 25-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 30 mi = 30 times 1760 = 52800 yd. Add the extra 0 yd to get the total in yards.

30 \times 1760 + 0 = 52800 + 0 = 52800 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 52800 yd in 25 minutes at a steady speed, so divide by 25 to get how far it goes each minute.

52800 \div 25 = 2112 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 60 minutes

#7 Identify Subproblems 4.MD.A.2

For 60 minutes, multiply the per-minute distance by 60.

2112 \times 60 = 126720 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 126720 yd by 1760 to find whole miles: 72 miles use 72 times 1760 = 126720 yd, leaving 126720 - 126720 = 0 yd. So the distance is 72 mi 0 yd.

126720 \div 1760 = 72 \text{ mi remainder } 0 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 72 mi 0 yd

4 · Reviewdoes it hold up?

60 minutes is more than 25 minutes, so the distance should be larger than 30 mi 0 yd, and 72 mi 0 yd is indeed larger. The car adds 2112 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 52800 yd covered in 25 min by $\frac{60}{25}$ to get 126720 yd = 72 mi 0 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 5 medium

A car travels $5 \text{ miles } 500 \text{ yards}$ in 10 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 22 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 5 mi 500 yd in 10 minutes at a steady speed. We must find how far it goes in 22 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 22, then convert back to miles and yards.

Givens

Distance in 10 min: 5 mi 500 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 22 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 10-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 5 mi = 5 times 1760 = 8800 yd. Add the extra 500 yd to get the total in yards.

5 \times 1760 + 500 = 8800 + 500 = 9300 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 9300 yd in 10 minutes at a steady speed, so divide by 10 to get how far it goes each minute.

9300 \div 10 = 930 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 22 minutes

#7 Identify Subproblems 4.MD.A.2

For 22 minutes, multiply the per-minute distance by 22.

930 \times 22 = 20460 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 20460 yd by 1760 to find whole miles: 11 miles use 11 times 1760 = 19360 yd, leaving 20460 - 19360 = 1100 yd. So the distance is 11 mi 1100 yd.

20460 \div 1760 = 11 \text{ mi remainder } 1100 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 11 mi 1100 yd

4 · Reviewdoes it hold up?

22 minutes is more than 10 minutes, so the distance should be larger than 5 mi 500 yd, and 11 mi 1100 yd is indeed larger. The car adds 930 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 9300 yd covered in 10 min by $\frac{22}{10}$ to get 20460 yd = 11 mi 1100 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 6 medium

A car travels $15 \text{ miles } 600 \text{ yards}$ in 12 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 18 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 15 mi 600 yd in 12 minutes at a steady speed. We must find how far it goes in 18 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 18, then convert back to miles and yards.

Givens

Distance in 12 min: 15 mi 600 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 18 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 12-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 15 mi = 15 times 1760 = 26400 yd. Add the extra 600 yd to get the total in yards.

15 \times 1760 + 600 = 26400 + 600 = 27000 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 27000 yd in 12 minutes at a steady speed, so divide by 12 to get how far it goes each minute.

27000 \div 12 = 2250 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 18 minutes

#7 Identify Subproblems 4.MD.A.2

For 18 minutes, multiply the per-minute distance by 18.

2250 \times 18 = 40500 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 40500 yd by 1760 to find whole miles: 23 miles use 23 times 1760 = 40480 yd, leaving 40500 - 40480 = 20 yd. So the distance is 23 mi 20 yd.

40500 \div 1760 = 23 \text{ mi remainder } 20 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 23 mi 20 yd

4 · Reviewdoes it hold up?

18 minutes is more than 12 minutes, so the distance should be larger than 15 mi 600 yd, and 23 mi 20 yd is indeed larger. The car adds 2250 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 27000 yd covered in 12 min by $\frac{18}{12}$ to get 40500 yd = 23 mi 20 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 7 hard

A car travels $18 \text{ miles } 900 \text{ yards}$ in 15 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 25 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 18 mi 900 yd in 15 minutes at a steady speed. We must find how far it goes in 25 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 25, then convert back to miles and yards.

Givens

Distance in 15 min: 18 mi 900 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 25 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 15-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 18 mi = 18 times 1760 = 31680 yd. Add the extra 900 yd to get the total in yards.

18 \times 1760 + 900 = 31680 + 900 = 32580 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 32580 yd in 15 minutes at a steady speed, so divide by 15 to get how far it goes each minute.

32580 \div 15 = 2172 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 25 minutes

#7 Identify Subproblems 4.MD.A.2

For 25 minutes, multiply the per-minute distance by 25.

2172 \times 25 = 54300 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 54300 yd by 1760 to find whole miles: 30 miles use 30 times 1760 = 52800 yd, leaving 54300 - 52800 = 1500 yd. So the distance is 30 mi 1500 yd.

54300 \div 1760 = 30 \text{ mi remainder } 1500 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 30 mi 1500 yd

4 · Reviewdoes it hold up?

25 minutes is more than 15 minutes, so the distance should be larger than 18 mi 900 yd, and 30 mi 1500 yd is indeed larger. The car adds 2172 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 32580 yd covered in 15 min by $\frac{25}{15}$ to get 54300 yd = 30 mi 1500 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 8 hard

A car travels $6 \text{ miles } 1056 \text{ yards}$ in 6 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 15 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 6 mi 1056 yd in 6 minutes at a steady speed. We must find how far it goes in 15 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 15, then convert back to miles and yards.

Givens

Distance in 6 min: 6 mi 1056 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 15 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 6-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 6 mi = 6 times 1760 = 10560 yd. Add the extra 1056 yd to get the total in yards.

6 \times 1760 + 1056 = 10560 + 1056 = 11616 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 11616 yd in 6 minutes at a steady speed, so divide by 6 to get how far it goes each minute.

11616 \div 6 = 1936 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 15 minutes

#7 Identify Subproblems 4.MD.A.2

For 15 minutes, multiply the per-minute distance by 15.

1936 \times 15 = 29040 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 29040 yd by 1760 to find whole miles: 16 miles use 16 times 1760 = 28160 yd, leaving 29040 - 28160 = 880 yd. So the distance is 16 mi 880 yd.

29040 \div 1760 = 16 \text{ mi remainder } 880 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 16 mi 880 yd

4 · Reviewdoes it hold up?

15 minutes is more than 6 minutes, so the distance should be larger than 6 mi 1056 yd, and 16 mi 880 yd is indeed larger. The car adds 1936 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 11616 yd covered in 6 min by $\frac{15}{6}$ to get 29040 yd = 16 mi 880 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Variant 9 hard

A car travels $8 \text{ miles } 1320 \text{ yards}$ in 10 minutes. If the car keeps driving at the same speed, how many miles and yards can it travel in 35 minutes?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A car goes 8 mi 1320 yd in 10 minutes at a steady speed. We must find how far it goes in 35 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 35, then convert back to miles and yards.

Givens

Distance in 10 min: 8 mi 1320 yd
The car keeps the same (constant) speed
1 mi = 1760 yd

Unknowns

The distance traveled in 35 minutes, in miles and yards

Constraints

Speed is constant, so distance grows in proportion to time
Distance must be in one unit (yards) before dividing and multiplying

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.

3 · Execute4 carry out the plan

1Convert the 10-minute distance to yards

#8 Analyze the Units 4.MD.A.1

Since 1 mi = 1760 yd, 8 mi = 8 times 1760 = 14080 yd. Add the extra 1320 yd to get the total in yards.

8 \times 1760 + 1320 = 14080 + 1320 = 15400 \text{ yd}

Working in a single unit (yards) makes the speed easy to compute.

2Find the distance per minute

#7 Identify Subproblems 3.OA.A.3

The car covers 15400 yd in 10 minutes at a steady speed, so divide by 10 to get how far it goes each minute.

15400 \div 10 = 1540 \text{ yd per minute}

A constant speed means the same number of yards is added every minute.

3Multiply by 35 minutes

#7 Identify Subproblems 4.MD.A.2

For 35 minutes, multiply the per-minute distance by 35.

1540 \times 35 = 53900 \text{ yd}

More time at the same speed means proportionally more distance.

4Convert back to miles and yards

#8 Analyze the Units 4.MD.A.1

Divide 53900 yd by 1760 to find whole miles: 30 miles use 30 times 1760 = 52800 yd, leaving 53900 - 52800 = 1100 yd. So the distance is 30 mi 1100 yd.

53900 \div 1760 = 30 \text{ mi remainder } 1100 \text{ yd}

Regrouping yards back into miles plus leftover yards gives the answer in the requested units.

Answer: 30 mi 1100 yd

4 · Reviewdoes it hold up?

35 minutes is more than 10 minutes, so the distance should be larger than 8 mi 1320 yd, and 30 mi 1100 yd is indeed larger. The car adds 1540 yd every minute at this steady speed.

Another way: Use the time ratio: scale the 15400 yd covered in 10 min by $\frac{35}{10}$ to get 53900 yd = 30 mi 1100 yd, confirming the per-minute method.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting between miles and yards using 1 mi = 1760 yd
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Finding the distance traveled in the new time at constant speed
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing to find yards per minute and multiplying by the new time

💡Takeaway. At a steady speed, find how far you go in one minute, then multiply by the new minutes - same speed, more time, more distance!

Distance grows in proportion to time · 9 practice problems

Generated variants — 9

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Where next?